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ruby/lib/matrix.rb

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#--
# matrix.rb -
# $Release Version: 1.0$
# $Revision: 1.13 $
# Original Version from Smalltalk-80 version
# on July 23, 1985 at 8:37:17 am
# by Keiju ISHITSUKA
#++
#
# = matrix.rb
#
# An implementation of Matrix and Vector classes.
#
# Author:: Keiju ISHITSUKA
# Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly))
#
# See classes Matrix and Vector for documentation.
#
require "e2mmap.rb"
module ExceptionForMatrix # :nodoc:
extend Exception2MessageMapper
def_e2message(TypeError, "wrong argument type %s (expected %s)")
def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)")
def_exception("ErrDimensionMismatch", "\#{self.name} dimension mismatch")
def_exception("ErrNotRegular", "Not Regular Matrix")
def_exception("ErrOperationNotDefined", "This operation(%s) can\\'t defined")
end
#
# The +Matrix+ class represents a mathematical matrix, and provides methods for creating
# special-case matrices (zero, identity, diagonal, singular, vector), operating on them
# arithmetically and algebraically, and determining their mathematical properties (trace, rank,
# inverse, determinant).
#
# Note that although matrices should theoretically be rectangular, this is not
# enforced by the class.
#
# Also note that the determinant of integer matrices may be incorrectly calculated unless you
# also <tt>require 'mathn'</tt>. This may be fixed in the future.
#
# == Method Catalogue
#
# To create a matrix:
# * <tt> Matrix[*rows] </tt>
# * <tt> Matrix.[](*rows) </tt>
# * <tt> Matrix.rows(rows, copy = true) </tt>
# * <tt> Matrix.columns(columns) </tt>
# * <tt> Matrix.diagonal(*values) </tt>
# * <tt> Matrix.scalar(n, value) </tt>
# * <tt> Matrix.scalar(n, value) </tt>
# * <tt> Matrix.identity(n) </tt>
# * <tt> Matrix.unit(n) </tt>
# * <tt> Matrix.I(n) </tt>
# * <tt> Matrix.zero(n) </tt>
# * <tt> Matrix.row_vector(row) </tt>
# * <tt> Matrix.column_vector(column) </tt>
#
# To access Matrix elements/columns/rows/submatrices/properties:
# * <tt> [](i, j) </tt>
# * <tt> #row_size </tt>
# * <tt> #column_size </tt>
# * <tt> #row(i) </tt>
# * <tt> #column(j) </tt>
# * <tt> #collect </tt>
# * <tt> #map </tt>
# * <tt> #minor(*param) </tt>
#
# Properties of a matrix:
# * <tt> #regular? </tt>
# * <tt> #singular? </tt>
# * <tt> #square? </tt>
#
# Matrix arithmetic:
# * <tt> *(m) </tt>
# * <tt> +(m) </tt>
# * <tt> -(m) </tt>
# * <tt> #/(m) </tt>
# * <tt> #inverse </tt>
# * <tt> #inv </tt>
# * <tt> ** </tt>
#
# Matrix functions:
# * <tt> #determinant </tt>
# * <tt> #det </tt>
# * <tt> #rank </tt>
# * <tt> #trace </tt>
# * <tt> #tr </tt>
# * <tt> #transpose </tt>
# * <tt> #t </tt>
#
# Conversion to other data types:
# * <tt> #coerce(other) </tt>
# * <tt> #row_vectors </tt>
# * <tt> #column_vectors </tt>
# * <tt> #to_a </tt>
#
# String representations:
# * <tt> #to_s </tt>
# * <tt> #inspect </tt>
#
class Matrix
@RCS_ID='-$Id: matrix.rb,v 1.13 2001/12/09 14:22:23 keiju Exp keiju $-'
# extend Exception2MessageMapper
include ExceptionForMatrix
# instance creations
private_class_method :new
#
# Creates a matrix where each argument is a row.
# Matrix[ [25, 93], [-1, 66] ]
# => 25 93
# -1 66
#
def Matrix.[](*rows)
new(:init_rows, rows, false)
end
#
# Creates a matrix where +rows+ is an array of arrays, each of which is a row
# to the matrix. If the optional argument +copy+ is false, use the given
# arrays as the internal structure of the matrix without copying.
# Matrix.rows([[25, 93], [-1, 66]])
# => 25 93
# -1 66
def Matrix.rows(rows, copy = true)
new(:init_rows, rows, copy)
end
#
# Creates a matrix using +columns+ as an array of column vectors.
# Matrix.columns([[25, 93], [-1, 66]])
# => 25 -1
# 93 66
#
#
def Matrix.columns(columns)
rows = (0 .. columns[0].size - 1).collect {|i|
(0 .. columns.size - 1).collect {|j|
columns[j][i]
}
}
Matrix.rows(rows, false)
end
#
# Creates a matrix where the diagonal elements are composed of +values+.
# Matrix.diagonal(9, 5, -3)
# => 9 0 0
# 0 5 0
# 0 0 -3
#
def Matrix.diagonal(*values)
size = values.size
rows = (0 .. size - 1).collect {|j|
row = Array.new(size).fill(0, 0, size)
row[j] = values[j]
row
}
rows(rows, false)
end
#
# Creates an +n+ by +n+ diagonal matrix where each diagonal element is
# +value+.
# Matrix.scalar(2, 5)
# => 5 0
# 0 5
#
def Matrix.scalar(n, value)
Matrix.diagonal(*Array.new(n).fill(value, 0, n))
end
#
# Creates an +n+ by +n+ identity matrix.
# Matrix.identity(2)
# => 1 0
# 0 1
#
def Matrix.identity(n)
Matrix.scalar(n, 1)
end
class << Matrix
alias unit identity
alias I identity
end
#
# Creates an +n+ by +n+ zero matrix.
# Matrix.zero(2)
# => 0 0
# 0 0
#
def Matrix.zero(n)
Matrix.scalar(n, 0)
end
#
# Creates a single-row matrix where the values of that row are as given in
# +row+.
# Matrix.row_vector([4,5,6])
# => 4 5 6
#
def Matrix.row_vector(row)
case row
when Vector
Matrix.rows([row.to_a], false)
when Array
Matrix.rows([row.dup], false)
else
Matrix.rows([[row]], false)
end
end
#
# Creates a single-column matrix where the values of that column are as given
# in +column+.
# Matrix.column_vector([4,5,6])
# => 4
# 5
# 6
#
def Matrix.column_vector(column)
case column
when Vector
Matrix.columns([column.to_a])
when Array
Matrix.columns([column])
else
Matrix.columns([[column]])
end
end
#
# This method is used by the other methods that create matrices, and is of no
# use to general users.
#
def initialize(init_method, *argv)
self.send(init_method, *argv)
end
def init_rows(rows, copy)
if copy
@rows = rows.collect{|row| row.dup}
else
@rows = rows
end
self
end
private :init_rows
#
# Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+.
#
def [](i, j)
@rows[i][j]
end
alias element []
alias component []
def []=(i, j, v)
@rows[i][j] = v
end
alias set_element []=
alias set_component []=
private :[]=, :set_element, :set_component
#
# Returns the number of rows.
#
def row_size
@rows.size
end
#
# Returns the number of columns. Note that it is possible to construct a
# matrix with uneven columns (e.g. Matrix[ [1,2,3], [4,5] ]), but this is
# mathematically unsound. This method uses the first row to determine the
# result.
#
def column_size
@rows[0].size
end
#
# Returns row vector number +i+ of the matrix as a Vector (starting at 0 like
# an array). When a block is given, the elements of that vector are iterated.
#
def row(i) # :yield: e
if block_given?
for e in @rows[i]
yield e
end
else
Vector.elements(@rows[i])
end
end
#
# Returns column vector number +j+ of the matrix as a Vector (starting at 0
# like an array). When a block is given, the elements of that vector are
# iterated.
#
def column(j) # :yield: e
if block_given?
0.upto(row_size - 1) do |i|
yield @rows[i][j]
end
else
col = (0 .. row_size - 1).collect {|i|
@rows[i][j]
}
Vector.elements(col, false)
end
end
#
# Returns a matrix that is the result of iteration of the given block over all
# elements of the matrix.
# Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
# => 1 4
# 9 16
#
def collect # :yield: e
rows = @rows.collect{|row| row.collect{|e| yield e}}
Matrix.rows(rows, false)
end
alias map collect
#
# Returns a section of the matrix. The parameters are either:
# * start_row, nrows, start_col, ncols; OR
# * col_range, row_range
#
# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
# => 9 0 0
# 0 5 0
#
def minor(*param)
case param.size
when 2
from_row = param[0].first
size_row = param[0].end - from_row
size_row += 1 unless param[0].exclude_end?
from_col = param[1].first
size_col = param[1].end - from_col
size_col += 1 unless param[1].exclude_end?
when 4
from_row = param[0]
size_row = param[1]
from_col = param[2]
size_col = param[3]
else
Matrix.Raise ArgumentError, param.inspect
end
rows = @rows[from_row, size_row].collect{|row|
row[from_col, size_col]
}
Matrix.rows(rows, false)
end
#--
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if this is a regular matrix.
#
def regular?
square? and rank == column_size
end
#
# Returns +true+ is this is a singular (i.e. non-regular) matrix.
#
def singular?
not regular?
end
#
# Returns +true+ is this is a square matrix. See note in column_size about this
# being unreliable, though.
#
def square?
column_size == row_size
end
#--
# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if and only if the two matrices contain equal elements.
#
def ==(other)
return false unless Matrix === other
other.compare_by_row_vectors(@rows)
end
def eql?(other)
return false unless Matrix === other
other.compare_by_row_vectors(@rows, :eql?)
end
#
# Not really intended for general consumption.
#
def compare_by_row_vectors(rows, comparison = :==)
return false unless @rows.size == rows.size
0.upto(@rows.size - 1) do |i|
return false unless @rows[i].send(comparison, rows[i])
end
true
end
#
# Returns a clone of the matrix, so that the contents of each do not reference
# identical objects.
#
def clone
Matrix.rows(@rows)
end
#
# Returns a hash-code for the matrix.
#
def hash
value = 0
for row in @rows
for e in row
value ^= e.hash
end
end
return value
end
#--
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Matrix multiplication.
# Matrix[[2,4], [6,8]] * Matrix.identity(2)
# => 2 4
# 6 8
#
def *(m) # m is matrix or vector or number
case(m)
when Numeric
rows = @rows.collect {|row|
row.collect {|e|
e * m
}
}
return Matrix.rows(rows, false)
when Vector
m = Matrix.column_vector(m)
r = self * m
return r.column(0)
when Matrix
Matrix.Raise ErrDimensionMismatch if column_size != m.row_size
rows = (0 .. row_size - 1).collect {|i|
(0 .. m.column_size - 1).collect {|j|
vij = 0
0.upto(column_size - 1) do |k|
vij += self[i, k] * m[k, j]
end
vij
}
}
return Matrix.rows(rows, false)
else
x, y = m.coerce(self)
return x * y
end
end
#
# Matrix addition.
# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
# => 6 0
# -4 12
#
def +(m)
case m
when Numeric
Matrix.Raise ErrOperationNotDefined, "+"
when Vector
m = Matrix.column_vector(m)
when Matrix
else
x, y = m.coerce(self)
return x + y
end
Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size
rows = (0 .. row_size - 1).collect {|i|
(0 .. column_size - 1).collect {|j|
self[i, j] + m[i, j]
}
}
Matrix.rows(rows, false)
end
#
# Matrix subtraction.
# Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
# => -8 2
# 8 1
#
def -(m)
case m
when Numeric
Matrix.Raise ErrOperationNotDefined, "-"
when Vector
m = Matrix.column_vector(m)
when Matrix
else
x, y = m.coerce(self)
return x - y
end
Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size
rows = (0 .. row_size - 1).collect {|i|
(0 .. column_size - 1).collect {|j|
self[i, j] - m[i, j]
}
}
Matrix.rows(rows, false)
end
#
# Matrix division (multiplication by the inverse).
# Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
# => -7 1
# -3 -6
#
def /(other)
case other
when Numeric
rows = @rows.collect {|row|
row.collect {|e|
e / other
}
}
return Matrix.rows(rows, false)
when Matrix
return self * other.inverse
else
x, y = other.coerce(self)
rerurn x / y
end
end
#
# Returns the inverse of the matrix.
# Matrix[[1, 2], [2, 1]].inverse
# => -1 1
# 0 -1
#
def inverse
Matrix.Raise ErrDimensionMismatch unless square?
Matrix.I(row_size).inverse_from(self)
end
alias inv inverse
#
# Not for public consumption?
#
def inverse_from(src)
size = row_size - 1
a = src.to_a
for k in 0..size
i = k
akk = a[k][k].abs
((k+1)..size).each do |j|
v = a[j][k].abs
if v > akk
i = j
akk = v
end
end
Matrix.Raise ErrNotRegular if akk == 0
if i != k
a[i], a[k] = a[k], a[i]
@rows[i], @rows[k] = @rows[k], @rows[i]
end
akk = a[k][k]
for i in 0 .. size
next if i == k
q = a[i][k].quo(akk)
a[i][k] = 0
for j in (k + 1).. size
a[i][j] -= a[k][j] * q
end
for j in 0..size
@rows[i][j] -= @rows[k][j] * q
end
end
for j in (k + 1).. size
a[k][j] = a[k][j].quo(akk)
end
for j in 0..size
@rows[k][j] = @rows[k][j].quo(akk)
end
end
self
end
#alias reciprocal inverse
#
# Matrix exponentiation. Defined for integer powers only. Equivalent to
# multiplying the matrix by itself N times.
# Matrix[[7,6], [3,9]] ** 2
# => 67 96
# 48 99
#
def ** (other)
if other.kind_of?(Integer)
x = self
if other <= 0
x = self.inverse
return Matrix.identity(self.column_size) if other == 0
other = -other
end
z = x
n = other - 1
while n != 0
while (div, mod = n.divmod(2)
mod == 0)
x = x * x
n = div
end
z *= x
n -= 1
end
z
elsif other.kind_of?(Float) || defined?(Rational) && other.kind_of?(Rational)
Matrix.Raise ErrOperationNotDefined, "**"
else
Matrix.Raise ErrOperationNotDefined, "**"
end
end
#--
# MATRIX FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns the determinant of the matrix. If the matrix is not square, the
# result is 0. This method's algorism is Gaussian elimination method
# and using Numeric#quo(). Beware that using Float values, with their
# usual lack of precision, can affect the value returned by this method. Use
# Rational values or Matrix#det_e instead if this is important to you.
#
# Matrix[[7,6], [3,9]].determinant
# => 63.0
#
def determinant
return 0 unless square?
size = row_size - 1
a = to_a
det = 1
k = 0
loop do
if (akk = a[k][k]) == 0
i = k
loop do
return 0 if (ii += 1) > size
break unless a[i][k] == 0
end
a[i], a[k] = a[k], a[i]
akk = a[k][k]
det *= -1
end
for i in k + 1 .. size
q = a[i][k].quo(akk)
(k + 1).upto(size) do |j|
a[i][j] -= a[k][j] * q
end
end
det *= akk
break unless (k += 1) <= size
end
det
end
alias det determinant
#
# Returns the determinant of the matrix. If the matrix is not square, the
# result is 0. This method's algorism is Gaussian elimination method.
# This method uses Euclidean algorism. If all elements are integer,
# really exact value. But, if an element is a float, can't return
# exact value.
#
# Matrix[[7,6], [3,9]].determinant
# => 63
#
def determinant_e
return 0 unless square?
size = row_size - 1
a = to_a
det = 1
k = 0
loop do
if a[k][k].zero?
i = k
loop do
return 0 if (i += 1) > size
break unless a[i][k].zero?
end
a[i], a[k] = a[k], a[i]
det *= -1
end
for i in (k + 1)..size
q = a[i][k].quo(a[k][k])
k.upto(size) do |j|
a[i][j] -= a[k][j] * q
end
unless a[i][k].zero?
a[i], a[k] = a[k], a[i]
det *= -1
redo
end
end
det *= a[k][k]
break unless (k += 1) <= size
end
det
end
alias det_e determinant_e
#
# Returns the rank of the matrix. Beware that using Float values,
# probably return faild value. Use Rational values or Matrix#rank_e
# for getting exact result.
#
# Matrix[[7,6], [3,9]].rank
# => 2
#
def rank
if column_size > row_size
a = transpose.to_a
a_column_size = row_size
a_row_size = column_size
else
a = to_a
a_column_size = column_size
a_row_size = row_size
end
rank = 0
k = 0
begin
if (akk = a[k][k]) == 0
i = k
exists = true
loop do
if (i += 1) > a_column_size - 1
exists = false
break
end
break unless a[i][k] == 0
end
if exists
a[i], a[k] = a[k], a[i]
akk = a[k][k]
else
i = k
exists = true
loop do
if (i += 1) > a_row_size - 1
exists = false
break
end
break unless a[k][i] == 0
end
if exists
k.upto(a_column_size - 1) do |j|
a[j][k], a[j][i] = a[j][i], a[j][k]
end
akk = a[k][k]
else
next
end
end
end
for i in (k + 1)..(a_row_size - 1)
q = a[i][k].quo(akk)
for j in (k + 1)..(a_column_size - 1)
a[i][j] -= a[k][j] * q
end
end
rank += 1
end while (k += 1) <= a_column_size - 1
return rank
end
#
# Returns the rank of the matrix. This method uses Euclidean
# algorism. If all elements are integer, really exact value. But, if
# an element is a float, can't return exact value.
#
# Matrix[[7,6], [3,9]].rank
# => 2
#
def rank_e
a = to_a
a_column_size = column_size
a_row_size = row_size
pi = 0
(0 ... a_column_size).each do |j|
if i = (pi ... a_row_size).find{|i0| !a[i0][j].zero?}
if i != pi
a[pi], a[i] = a[i], a[pi]
end
(pi + 1 ... a_row_size).each do |k|
q = a[k][j].quo(a[pi][j])
(pi ... a_column_size).each do |j0|
a[k][j0] -= q * a[pi][j0]
end
if k > pi && !a[k][j].zero?
a[k], a[pi] = a[pi], a[k]
redo
end
end
pi += 1
end
end
pi
end
#
# Returns the trace (sum of diagonal elements) of the matrix.
# Matrix[[7,6], [3,9]].trace
# => 16
#
def trace
tr = 0
0.upto(column_size - 1) do |i|
tr += @rows[i][i]
end
tr
end
alias tr trace
#
# Returns the transpose of the matrix.
# Matrix[[1,2], [3,4], [5,6]]
# => 1 2
# 3 4
# 5 6
# Matrix[[1,2], [3,4], [5,6]].transpose
# => 1 3 5
# 2 4 6
#
def transpose
Matrix.columns(@rows)
end
alias t transpose
#--
# CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# FIXME: describe #coerce.
#
def coerce(other)
case other
when Numeric
return Scalar.new(other), self
else
raise TypeError, "#{self.class} can't be coerced into #{other.class}"
end
end
#
# Returns an array of the row vectors of the matrix. See Vector.
#
def row_vectors
rows = (0 .. row_size - 1).collect {|i|
row(i)
}
rows
end
#
# Returns an array of the column vectors of the matrix. See Vector.
#
def column_vectors
columns = (0 .. column_size - 1).collect {|i|
column(i)
}
columns
end
#
# Returns an array of arrays that describe the rows of the matrix.
#
def to_a
@rows.collect{|row| row.collect{|e| e}}
end
def elements_to_f
collect{|e| e.to_f}
end
def elements_to_i
collect{|e| e.to_i}
end
def elements_to_r
collect{|e| e.to_r}
end
#--
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Overrides Object#to_s
#
def to_s
"Matrix[" + @rows.collect{|row|
"[" + row.collect{|e| e.to_s}.join(", ") + "]"
}.join(", ")+"]"
end
#
# Overrides Object#inspect
#
def inspect
"Matrix"+@rows.inspect
end
# Private CLASS
class Scalar < Numeric # :nodoc:
include ExceptionForMatrix
def initialize(value)
@value = value
end
# ARITHMETIC
def +(other)
case other
when Numeric
Scalar.new(@value + other)
when Vector, Matrix
Scalar.Raise WrongArgType, other.class, "Numeric or Scalar"
when Scalar
Scalar.new(@value + other.value)
else
x, y = other.coerce(self)
x + y
end
end
def -(other)
case other
when Numeric
Scalar.new(@value - other)
when Vector, Matrix
Scalar.Raise WrongArgType, other.class, "Numeric or Scalar"
when Scalar
Scalar.new(@value - other.value)
else
x, y = other.coerce(self)
x - y
end
end
def *(other)
case other
when Numeric
Scalar.new(@value * other)
when Vector, Matrix
other.collect{|e| @value * e}
else
x, y = other.coerce(self)
x * y
end
end
def / (other)
case other
when Numeric
Scalar.new(@value / other)
when Vector
Scalar.Raise WrongArgType, other.class, "Numeric or Scalar or Matrix"
when Matrix
self * other.inverse
else
x, y = other.coerce(self)
x.quo(y)
end
end
def ** (other)
case other
when Numeric
Scalar.new(@value ** other)
when Vector
Scalar.Raise WrongArgType, other.class, "Numeric or Scalar or Matrix"
when Matrix
other.powered_by(self)
else
x, y = other.coerce(self)
x ** y
end
end
end
end
#
# The +Vector+ class represents a mathematical vector, which is useful in its own right, and
# also constitutes a row or column of a Matrix.
#
# == Method Catalogue
#
# To create a Vector:
# * <tt> Vector.[](*array) </tt>
# * <tt> Vector.elements(array, copy = true) </tt>
#
# To access elements:
# * <tt> [](i) </tt>
#
# To enumerate the elements:
# * <tt> #each2(v) </tt>
# * <tt> #collect2(v) </tt>
#
# Vector arithmetic:
# * <tt> *(x) "is matrix or number" </tt>
# * <tt> +(v) </tt>
# * <tt> -(v) </tt>
#
# Vector functions:
# * <tt> #inner_product(v) </tt>
# * <tt> #collect </tt>
# * <tt> #map </tt>
# * <tt> #map2(v) </tt>
# * <tt> #r </tt>
# * <tt> #size </tt>
#
# Conversion to other data types:
# * <tt> #covector </tt>
# * <tt> #to_a </tt>
# * <tt> #coerce(other) </tt>
#
# String representations:
# * <tt> #to_s </tt>
# * <tt> #inspect </tt>
#
class Vector
include ExceptionForMatrix
#INSTANCE CREATION
private_class_method :new
#
# Creates a Vector from a list of elements.
# Vector[7, 4, ...]
#
def Vector.[](*array)
new(:init_elements, array, copy = false)
end
#
# Creates a vector from an Array. The optional second argument specifies
# whether the array itself or a copy is used internally.
#
def Vector.elements(array, copy = true)
new(:init_elements, array, copy)
end
#
# For internal use.
#
def initialize(method, array, copy)
self.send(method, array, copy)
end
#
# For internal use.
#
def init_elements(array, copy)
if copy
@elements = array.dup
else
@elements = array
end
end
# ACCESSING
#
# Returns element number +i+ (starting at zero) of the vector.
#
def [](i)
@elements[i]
end
alias element []
alias component []
def []=(i, v)
@elements[i]= v
end
alias set_element []=
alias set_component []=
private :[]=, :set_element, :set_component
#
# Returns the number of elements in the vector.
#
def size
@elements.size
end
#--
# ENUMERATIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Iterate over the elements of this vector and +v+ in conjunction.
#
def each2(v) # :yield: e1, e2
Vector.Raise ErrDimensionMismatch if size != v.size
0.upto(size - 1) do |i|
yield @elements[i], v[i]
end
end
#
# Collects (as in Enumerable#collect) over the elements of this vector and +v+
# in conjunction.
#
def collect2(v) # :yield: e1, e2
Vector.Raise ErrDimensionMismatch if size != v.size
(0 .. size - 1).collect do |i|
yield @elements[i], v[i]
end
end
#--
# COMPARING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ iff the two vectors have the same elements in the same order.
#
def ==(other)
return false unless Vector === other
other.compare_by(@elements)
end
def eql?(other)
return false unless Vector === other
other.compare_by(@elements, :eql?)
end
#
# For internal use.
#
def compare_by(elements, comparison = :==)
@elements.send(comparison, elements)
end
#
# Return a copy of the vector.
#
def clone
Vector.elements(@elements)
end
#
# Return a hash-code for the vector.
#
def hash
@elements.hash
end
#--
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Multiplies the vector by +x+, where +x+ is a number or another vector.
#
def *(x)
case x
when Numeric
els = @elements.collect{|e| e * x}
Vector.elements(els, false)
when Matrix
Matrix.column_vector(self) * x
else
s, x = x.coerce(self)
s * x
end
end
#
# Vector addition.
#
def +(v)
case v
when Vector
Vector.Raise ErrDimensionMismatch if size != v.size
els = collect2(v) {|v1, v2|
v1 + v2
}
Vector.elements(els, false)
when Matrix
Matrix.column_vector(self) + v
else
s, x = v.coerce(self)
s + x
end
end
#
# Vector subtraction.
#
def -(v)
case v
when Vector
Vector.Raise ErrDimensionMismatch if size != v.size
els = collect2(v) {|v1, v2|
v1 - v2
}
Vector.elements(els, false)
when Matrix
Matrix.column_vector(self) - v
else
s, x = v.coerce(self)
s - x
end
end
#--
# VECTOR FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns the inner product of this vector with the other.
# Vector[4,7].inner_product Vector[10,1] => 47
#
def inner_product(v)
Vector.Raise ErrDimensionMismatch if size != v.size
p = 0
each2(v) {|v1, v2|
p += v1 * v2
}
p
end
#
# Like Array#collect.
#
def collect # :yield: e
els = @elements.collect {|v|
yield v
}
Vector.elements(els, false)
end
alias map collect
#
# Like Vector#collect2, but returns a Vector instead of an Array.
#
def map2(v) # :yield: e1, e2
els = collect2(v) {|v1, v2|
yield v1, v2
}
Vector.elements(els, false)
end
#
# Returns the modulus (Pythagorean distance) of the vector.
# Vector[5,8,2].r => 9.643650761
#
def r
v = 0
for e in @elements
v += e*e
end
return Math.sqrt(v)
end
#--
# CONVERTING
#++
#
# Creates a single-row matrix from this vector.
#
def covector
Matrix.row_vector(self)
end
#
# Returns the elements of the vector in an array.
#
def to_a
@elements.dup
end
def elements_to_f
collect{|e| e.to_f}
end
def elements_to_i
collect{|e| e.to_i}
end
def elements_to_r
collect{|e| e.to_r}
end
#
# FIXME: describe Vector#coerce.
#
def coerce(other)
case other
when Numeric
return Matrix::Scalar.new(other), self
else
raise TypeError, "#{self.class} can't be coerced into #{other.class}"
end
end
#--
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Overrides Object#to_s
#
def to_s
"Vector[" + @elements.join(", ") + "]"
end
#
# Overrides Object#inspect
#
def inspect
str = "Vector"+@elements.inspect
end
end
# Documentation comments:
# - Matrix#coerce and Vector#coerce need to be documented
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